Need to Know Flashcards
The Commutative Property
a+b=b+a ; ab=ba
The Associative Property
(a+b) +c = a+(b+c) ; (ab)c = a(bc)
The Distributive Property
a*(b+c) = ab+ac
The Commutative and Associative Properties do not work with
Subtraction or Division
Prime Numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 and 59
Factorization for 21
3 and 7 are prime factors
Greatest Common Factor (GCF) of 56 and 70
The factorization of 56 is = 2227
The factorization of 70 is = 257
The two largest numbers in both is 27 = 14
Least Common Factor (LCF) of 9 and 15
The factorization of 9 is = 33
The factorization of 15 is = 35
Multiply the shared primes (3*3) by the unshared primes (5) = 45
The absolute value is…
The positive form of the number
|x| and |-x| are equal to
x
To find some part of a whole use
Part Percent
——– = ———–
Whole 100
Percent Change
(Change * 100)
%change = ———————
Original
Exponent Laws:
A B x * x equals
(A+B)
x
Exponent Laws:
A X --------- B X equals
(A-B)
X
Exponent Laws:
B
A
X equals
(A*B)
X
1 raised to any power is
1
0 raised to any nonzero power is
0
Any number raised to the power of 0 is
1
Fractions as Exponents:
1/2
x equals
__
√ x
Fractions as Exponents:
2/3 x equals
_____
1 | 2
√ x
Negative Exponents:
-1
x equals
x
Negative Exponents:
-2
x equals
2
x
A negative number raised to an even power is
positive
A negative number raised to an odd power is
negative
Odd/Even Exponents:
3 x = 8 means x =
2
Odd/Even Exponents:
4 x = 16 means x =
2 or it can equal -2
Simplifying Expressions:
6xy + 5x) - (4xy - 3y
You are able to subtract the like variables and keep the other variables the same.
This equals = 2yx+5x+3y
Multiply Monomials:
3 2 5y * 6y equals
5
30y
Multiplying Polynomials:
(x+2) (x+7) =
Use the FOIL (First, Inner, Outer, Last) Method:
2
x +9x + 14
Factoring Using GCF:
3 2 6x + 12x +33x =
2
3x(2x +4x +11)
Solving Equations:
What you do to one side
You must also do to the other.
Eliminating Fractions:
a b
—- * —–
b a is equal to
1
Eliminating Fractions:
2
—- x = 8
5
Multiply the fraction to make it one. What you do to one side must also be done to the other.
2 5 5 |
—— * —– X = —- 8 | X = 20
5 2 2 |
Find the Lowest Common Denominator:
3x 1 x
—- + —- = —-
4 2 3
The LCD is 12, multiply the top by 12 to get:
36x 12 12x |
——- + ——- = ——– | 9x + 6 = 4x solve for x
4 2 3 |
Cross Multiplication:
a c
— = —
b d can be written
ad = bc
Two Variables/Systems of Equations:
SUBSTITUTION METHOD
3x + y = 17 and 2x - 2y = 6
1). Solve for y in one equation
3x + y = 17 (subtract 3x)
y = 17 - 3x
2). Input the solution for y into the other problem:
2x - 2 (17 - 3x) = 6
2x + 6x - 34 = 6
8x = 40 divid by 8 | x = 5Two Variables/Systems of Equations:
ELIMINATION METHOD
3x + y = 17 and 2x - 2y = 6
1). Line the equations up on-top of each other:
3x + y = 17
2x - 2y = 6
2). My the two “y”s cancel by multiplying by 2:
2(3x + y) = 2(17)
6x + 2y = 34
3). Line the problems up again and solve:
6x + 2y = 34
+ 2x - 2y = 6
8x = 40 | solve for x
If two lines intersect what is the sum of the four resulting angles?
360
Polygon
Any figure with three or more sides
The total degrees of a polygon:
total degrees = 180 (n-2) where n = # of sides
The Area of a Triangle
1
Area = – b*h
2
Special Right Triangle:
45-45-90
Leg1 : Leg2 : Hypotenuse
x : x : x√2
Special Right Triangle:
30-60-90
Leg1 : Leg2 : Hypotenuse
x : x√3 : 2x
Pythagorean Triples
3 - 4 - 5
5 - 12 - 13
8 - 15 - 17
7 - 24 - 25
The Area of Circle
2
Area = π*r
Circumference of a Circle
Circumference = 2πr
Arc Length
r
Arc Length = ——- 2πr
360
Area of a Sector
r 2
Area of sector = ——- π*r
360
If two inscribed angles hold the same chord…
the two inscribed angles are equal
A chord is…
a line segments between two points on a circle
An inscribed angle holding the diameter is…
a right angle
The Perimeter of a Square
perimeter = 4s , where 2 = side
The Area of a Square
2
area = s
The Area of a Rectangle
area = L*W
The Perimeter of a Rectangle
perimeter = 2L+2W
The Area of a Trapezoid
base1 * base2
area = ———————— x height
2
The Volume of a Cube
3
volume = s
The Surface Area of a Cube
2
surface area = 6s
The volume of a cube and the surface area of a cube are equal when s (the side length) =
6
The Area of a Rectangular Solid
volume = heightdepthwidth
The Surface Area of a Rectangular Solid
2HW + 2HW + 2HW
The Volume of a Cylinder
2
volume = r * π * H
The Surface Area of a Cylinder
2
surface area = 2πr + 2πr*h
The slope of any line can be found
by substracting the y values of a pair and dividing it by the difference in the x values:
(y2 - y1)
slope = m =————–
(x2 - x1)
To find the y intercept plug in
0 for x and solve for y
The Distance Formula
___________________
√ 2 2
√(x2 - x1) + (y2 - y1)
Distance
rate
distance = ———-
time
Rate
distance
rate = ————–
time
Time
rate
time = ————
distance
Average Speed
total distance traveled
average speed = ——————————–
total time
Work Rate:
OUTPUT
output = rate * time
Work Rate:
TOTAL WORK
1 1 1
————— = —————– + —————–
TotalWork WorkRate1 WorkRate2
Simple Interest
( RT )
Interest = P ( 1+ —– )
( 100 )
where p is principal, rate, time
Compound Interest
nt
( r )
Interest = P ( 1+ --------- )
( 100n )
where n = the number of time compounded per year.Mean
The average of all the numbers: total sum
————-
n
Median
The middle most value, for even amount of numbers use the average of the two
Mode
The number that occurs most frequently
Weighted Average
(proportion)(group A average) + (proportion)(group B average) … etc
Range
greatest value - least value
Standard Deviation
_____________________
√ 2 2 2
√ (a-m) + (b-m) + (c-m)
SD =√————————————- etc
√ n
Probability that event A will happen:
number of outcomes where A occurs
P(A) = ——————————————————-
total number of outcomes
The chance that the event does not occur:
P(event happens) + P(event does not happen) = 1
Mutually Exclusive Events:
Events that cannot happen together; P (A and B) = 0
Events A and B (if they are independent events):
P (A and B) = P(A) * P(B)
Events A or B happens or A and B happens:
P ( A or B) = P(A) + P(B) - P(A - B)
